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@misc{Foley96,
	author = {Foley, James D and van Dam, Andries and Feiner, Steven K and Hughes, John F},
	date-added = {2021-08-20 13:23:10 -0400},
	date-modified = {2021-08-20 13:23:10 -0400},
	publisher = {Addison-Wesley, Reading, Massachusetts},
	title = {Computer Graphics: Principles and Pract Edition},
	year = {1996}}

@article{Zavarise09,
	author = {Zavarise, Giorgio and De Lorenzis, Laura},
	date-added = {2021-08-20 13:14:58 -0400},
	date-modified = {2021-08-20 13:14:58 -0400},
	journal = {Computer Methods in Applied Mechanics and Engineering},
	number = {41},
	pages = {3428--3451},
	publisher = {Elsevier},
	title = {The node-to-segment algorithm for 2D frictionless contact: classical formulation and special cases},
	volume = {198},
	year = {2009}}

@article{Tur09,
	author = {Tur, M and Fuenmayor, FJ and Wriggers, P},
	date-added = {2021-08-20 13:14:35 -0400},
	date-modified = {2021-08-20 13:14:35 -0400},
	journal = {Computer Methods in Applied Mechanics and Engineering},
	number = {37},
	pages = {2860--2873},
	publisher = {Elsevier},
	title = {A mortar-based frictional contact formulation for large deformations using Lagrange multipliers},
	volume = {198},
	year = {2009}}

@article{Simo92c,
	author = {Simo, J Ci and Laursen, TA},
	date-added = {2021-08-20 11:45:00 -0400},
	date-modified = {2021-08-20 11:45:04 -0400},
	journal = {Computers \&amp; Structures},
	number = {1},
	pages = {97--116},
	publisher = {Elsevier},
	title = {An augmented Lagrangian treatment of contact problems involving friction},
	volume = {42},
	year = {1992}}

@article{Giannakopoulos89,
	author = {Giannakopoulos, AE},
	date-added = {2021-08-20 11:44:02 -0400},
	date-modified = {2021-08-20 11:44:02 -0400},
	journal = {Computers \&amp; structures},
	number = {1},
	pages = {157--167},
	publisher = {Elsevier},
	title = {The return mapping method for the integration of friction constitutive relations},
	volume = {32},
	year = {1989}}

@book{Wriggers06,
	address = {Berlin},
	annote = {LDR    01893cam  22003377a 4500
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010    $a  2006922005
020    $a9783540326083 (acid-free paper)
020    $a3540326081 (acid-free paper)
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050 00 $aTA353$b.W75 2006
082 00 $a620.1/05$222
100 1  $aWriggers, P.
245 10 $aComputational contact mechanics /$cPeter Wriggers.
250    $a2nd ed.
260    $aBerlin ;$aNew York :$bSpringer,$cc2006.
300    $axii, 518 p. :$bill. ;$c24 cm.
504    $aIncludes bibliographical references (p. [487]-512) and index.
505 00 $aIntroduction to contact mechanics -- Continuum solid mechanics and weak forms -- Contact kinematics -- Constitutive equations for contact interfaces -- Contact boundary value problem and weak form -- Discretization of the continuum --  Discretization, small deformation contact --$tDiscretization, large deformation contact -- Solution algorithms -- Thermo-mechanical contact -- Beam contact -- Computation of critical points with contact constraints -- Adaptive finite element methods for contact problems.
650  0 $aContact mechanics$xMathematical models.
856 42 $3Publisher description$uhttp://www.loc.gov/catdir/enhancements/fy0663/2006922005-d.html
856 42 $3Contributor biographical information$uhttp://www.loc.gov/catdir/enhancements/fy0824/2006922005-b.html
856 41 $3Table of contents only$uhttp://www.loc.gov/catdir/enhancements/fy0824/2006922005-t.html
},
	author = {Wriggers, P},
	call-number = {TA353},
	date-added = {2021-08-20 11:43:40 -0400},
	date-modified = {2021-08-20 11:43:40 -0400},
	dewey-call-number = {620.1/05},
	edition = {2nd ed},
	genre = {Contact mechanics},
	isbn = {9783540326083 (acid-free paper)},
	library-id = {2006922005},
	publisher = {Springer},
	title = {Computational contact mechanics},
	url = {http://www.loc.gov/catdir/enhancements/fy0663/2006922005-d.html},
	year = {2006},
	Bdsk-Url-1 = {http://www.loc.gov/catdir/enhancements/fy0663/2006922005-d.html}}

@article{Saracibar97,
	author = {de Saracibar, C Agelet},
	date-added = {2021-08-20 11:43:11 -0400},
	date-modified = {2021-08-20 11:43:11 -0400},
	journal = {Computer Methods in Applied Mechanics and Engineering},
	number = {3-4},
	pages = {303--334},
	publisher = {Elsevier},
	title = {A new frictional time integration algorithm for large slip multi-body frictional contact problems},
	volume = {142},
	year = {1997}}

@article{Sauer15,
	author = {Sauer, Roger A and De Lorenzis, Laura},
	date-added = {2021-08-20 11:43:00 -0400},
	date-modified = {2021-08-20 11:43:00 -0400},
	journal = {International Journal for Numerical Methods in Engineering},
	number = {4},
	pages = {251--280},
	publisher = {Wiley Online Library},
	title = {An unbiased computational contact formulation for 3D friction},
	volume = {101},
	year = {2015}}

@article{Wriggers90,
	author = {Wriggers, Peter and Van, T Vu and Stein, Erwin},
	date-added = {2021-08-20 11:42:46 -0400},
	date-modified = {2021-08-20 11:42:46 -0400},
	journal = {Computers \&amp; Structures},
	number = {3},
	pages = {319--331},
	publisher = {Elsevier},
	title = {Finite element formulation of large deformation impact-contact problems with friction},
	volume = {37},
	year = {1990}}

@article{Poulios15,
	author = {Poulios, Konstantinos and Renard, Yves},
	date-added = {2021-08-20 11:42:11 -0400},
	date-modified = {2021-08-20 11:42:11 -0400},
	journal = {Computers \&amp; Structures},
	pages = {75--90},
	publisher = {Elsevier},
	title = {An unconstrained integral approximation of large sliding frictional contact between deformable solids},
	volume = {153},
	year = {2015}}

@book{Bertsekas82,
	address = {New York},
	annote = {LDR    00899pam  2200265 a 4500
001    4679673
005    19830126000000.0
008    811008s1982    nyua     b    001 0 eng  
035    $9(DLC)   81017612
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010    $a   81017612 
020    $a0120934809
040    $aDLC$cDLC$dDLC
050 00 $aQA402.5$b.B46 1982
082 00 $a519.4$219
100 1  $aBertsekas, Dimitri P.
245 10 $aConstrained optimization and Lagrange multiplier methods /$cDimitri P. Bertsekas.
260    $aNew York :$bAcademic Press,$c1982.
300    $axiii, 395 p. :$bill. ;$c24 cm.
440  0 $aComputer science and applied mathematics
504    $aBibliography: p. 383-392.
500    $aIncludes index.
650  0 $aMathematical optimization.
650  0 $aMultipliers (Mathematical analysis)
991    $bc-GenColl$hQA402.5$i.B46 1982$p00009887635$tCopy 1$wBOOKS
},
	author = {Bertsekas, Dimitri P},
	call-number = {QA402.5},
	date-added = {2021-08-20 11:18:29 -0400},
	date-modified = {2021-08-20 11:18:29 -0400},
	dewey-call-number = {519.4},
	genre = {Mathematical optimization},
	isbn = {0120934809},
	library-id = {81017612},
	publisher = {Academic Press},
	title = {Constrained optimization and Lagrange multiplier methods},
	year = {1982}}

@incollection{Curnier95,
	author = {Curnier, Alain and He, Qi-Chang and Klarbring, Anders},
	booktitle = {Contact mechanics},
	date-added = {2021-08-20 11:15:58 -0400},
	date-modified = {2021-08-20 11:15:58 -0400},
	pages = {145--158},
	publisher = {Springer},
	title = {Continuum mechanics modelling of large deformation contact with friction},
	year = {1995}}

@book{Wriggers07,
	address = {Wien},
	annote = {LDR    01962cam  22003497a 4500
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955    $ajp00 2008-05-23 z-processor to ASCD/CCPT$ijx12 2008-06-09$ejx12 2008-06-09 to BCCD
955    $apv19 2008-04-26 to ASCD$ajp00 2008-04-29
010    $a  2008273250
020    $a9783211772973
020    $a3211772979
035    $a(OCoLC)ocn192081393
040    $aOHX$cOHX$dYDXCP$dBAKER$dGAT$dCOO$dDLC
042    $alccopycat
050 00 $aTA353$b.C64 2007
082 04 $a620.105
245 00 $aComputational contact mechanics /$cedited by Peter Wriggers, Tod A. Laursen.
260    $aWien ;$aNew York :$bSpringer,$cc2007.
300    $a248 p. :$bill. (some col.) ;$c25 cm.
490 1  $aCISM courses and lectures ;$vno. 498
504    $aIncludes bibliographical references.
505 0  $aEmerging spatial and temporal discretization methods in contact and impact mechanics / T.A. Laursen -- Reliability of micromechanical contact models: a still open issue / G. Zavarise and M. Paggi -- Modern approaches on rolling contact / M. Brinkmeier, U. Nackenhorst and M. Ziefle -- Homogenization and multi-scale approaches for contact problems / P. Wriggers and J. Nettingsmeier -- Contact on multiprocessor environment: from mulitcontact problems to multiscale approaches / P. Alart -- Numerical soil mechanics experiments using discontinuous deformation analysis / J.L. P{\'e}rez Aparicio and R. B. Pareja.
650  0 $aContact mechanics$xMathematical models.
700 1  $aWriggers, P.
700 1  $aLaursen, Tod A.
830  0 $aCourses and lectures ;$vno. 498.
856 42 $3Publisher description$uhttp://www.loc.gov/catdir/enhancements/fy0904/2008273250-d.html
856 41 $3Table of contents only$uhttp://www.loc.gov/catdir/enhancements/fy0904/2008273250-t.html
},
	author = {Wriggers, P and Laursen, Tod A},
	call-number = {TA353},
	date-added = {2021-08-20 11:15:46 -0400},
	date-modified = {2021-08-20 11:15:46 -0400},
	dewey-call-number = {620.105},
	genre = {Contact mechanics},
	isbn = {9783211772973},
	library-id = {2008273250},
	publisher = {Springer},
	series = {CISM courses and lectures},
	title = {Computational contact mechanics},
	volume = {no. 498},
	year = {2007},
	Bdsk-Url-1 = {http://www.loc.gov/catdir/enhancements/fy0904/2008273250-d.html}}

@article{Zimmerman18,
	abstract = {This study formulates a finite element algorithm for frictional contact of solid materials, accommodating finite deformation and sliding. The algorithm uses a penalty method regularized with an augmented Lagrangian scheme to enforce contact constraints in a nonmortar surface-to-surface approach. Use of a novel kinematical approach to contact detection and enforcement of frictional constraints allows solution of complex problems previously requiring mortar methods or contact smoothing algorithms. Patch tests are satisfied to a high degree of accuracy with a single-pass penalty method, ensuring formulation errors do not affect the solution. The accuracy of the implementation is verified with Hertzian contact, and illustrations demonstrating the ability to handle large deformations and sliding are presented and validated against prior literature. A biomechanically relevant example addressing finger friction during grasping demonstrates the utility of the proposed algorithm. The algorithm is implemented in the open source software febio, and the source code is made available to the general public.},
	author = {Zimmerman, Brandon K and Ateshian, Gerard A},
	date-added = {2021-08-20 11:02:59 -0400},
	date-modified = {2021-08-20 11:02:59 -0400},
	doi = {10.1115/1.4040497},
	journal = {J Biomech Eng},
	journal-full = {Journal of biomechanical engineering},
	mesh = {Algorithms; Biomechanical Phenomena; Finite Element Analysis; Friction; Surface Properties},
	month = {08},
	number = {8},
	pmc = {PMC6056201},
	pmid = {30003262},
	pst = {ppublish},
	title = {A Surface-to-Surface Finite Element Algorithm for Large Deformation Frictional Contact in febio},
	volume = {140},
	year = {2018},
	Bdsk-Url-1 = {https://doi.org/10.1115/1.4040497}}

@article{Ateshian09b,
	abstract = {Over the last two decades, considerable progress has been reported in the field of cartilage mechanics that impacts our understanding of the role of interstitial fluid pressurization on cartilage lubrication. Theoretical and experimental studies have demonstrated that the interstitial fluid of cartilage pressurizes considerably under loading, potentially supporting most of the applied load under various transient or steady-state conditions. The fraction of the total load supported by fluid pressurization has been called the fluid load support. Experimental studies have demonstrated that the friction coefficient of cartilage correlates negatively with this variable, achieving remarkably low values when the fluid load support is greatest. A theoretical framework that embodies this relationship has been validated against experiments, predicting and explaining various outcomes, and demonstrating that a low friction coefficient can be maintained for prolonged loading durations under normal physiological function. This paper reviews salient aspects of this topic, as well as its implications for improving our understanding of boundary lubrication by molecular species in synovial fluid and the cartilage superficial zone. Effects of cartilage degeneration on its frictional response are also reviewed.},
	author = {Ateshian, Gerard A},
	date-added = {2021-08-20 11:02:05 -0400},
	date-modified = {2021-08-20 11:02:05 -0400},
	doi = {10.1016/j.jbiomech.2009.04.040},
	journal = {J Biomech},
	journal-full = {Journal of biomechanics},
	mesh = {Animals; Cartilage, Articular; Chondroitin ABC Lyase; Compressive Strength; Extracellular Fluid; Friction; Humans; Stress, Mechanical; Synovial Fluid},
	month = {Jun},
	number = {9},
	pages = {1163-76},
	pmc = {PMC2758165},
	pmid = {19464689},
	pst = {ppublish},
	title = {The role of interstitial fluid pressurization in articular cartilage lubrication},
	volume = {42},
	year = {2009},
	Bdsk-Url-1 = {https://doi.org/10.1016/j.jbiomech.2009.04.040}}

@article{Zimmerman21a,
	abstract = {The frictional response of porous and permeable hydrated biological tissues such as articular cartilage is significantly dependent on interstitial fluid pressurization. To model this response, it is common to represent such tissues as biphasic materials, consisting of a binary mixture of a porous solid matrix and an interstitial fluid. However, no computational algorithms currently exist in either commercial or open-source software that can model frictional contact between such materials. Therefore, this study formulates and implements a finite element algorithm for large deformation biphasic frictional contact in the open-source finite element software FEBio. This algorithm relies on a local form of a biphasic friction model that has been previously validated against experiments, and implements the model into our recently-developed surface-to-surface contact algorithm. Contact constraints, including those specific to pressurized porous media, are enforced with the penalty method regularized with an active-passive augmented Lagrangian scheme. Numerical difficulties specific to challenging finite deformation biphasic contact problems are overcome with novel smoothing schemes for fluid pressures and Lagrange multipliers. Implementation accuracy is verified against semi-analytical solutions for biphasic frictional contact, with extensive validation performed using canonical cartilage friction experiments from prior literature. Essential details of the formulation are provided in this paper, and the source code of this biphasic frictional contact algorithm is made available to the general public.},
	author = {Zimmerman, Brandon and Maas, Steve A and Weiss, Jeffrey A and Ateshian, Gerard A},
	date-added = {2021-08-16 13:59:48 -0400},
	date-modified = {2021-08-16 13:59:56 -0400},
	doi = {10.1115/1.4052114},
	journal = {J Biomech Eng},
	journal-full = {Journal of biomechanical engineering},
	month = {Aug},
	pmid = {34382640},
	pst = {aheadofprint},
	title = {A Finite Element Algorithm for Large Deformation Biphasic Frictional Contact Between Porous-Permeable Hydrated Soft Tissues},
	year = {2021},
	Bdsk-Url-1 = {https://doi.org/10.1115/1.4052114}}

@article{Kiousis08,
	author = {Kiousis, DE and Gasser, TC and Holzapfel, GA},
	date-added = {2021-08-16 11:00:46 -0400},
	date-modified = {2021-08-16 11:00:57 -0400},
	journal = {International journal for numerical methods in engineering},
	number = {7},
	pages = {826--855},
	publisher = {Wiley Online Library},
	title = {Smooth contact strategies with emphasis on the modeling of balloon angioplasty with stenting},
	volume = {75},
	year = {2008}}

@article{Kiousis09,
	author = {Kiousis, Dimitrios E and Wulff, Alexander R and Holzapfel, Gerhard A},
	date-added = {2021-08-16 11:00:32 -0400},
	date-modified = {2021-08-16 11:00:57 -0400},
	journal = {Annals of Biomedical Engineering},
	number = {2},
	pages = {315--330},
	publisher = {Springer},
	title = {Experimental studies and numerical analysis of the inflation and interaction of vascular balloon catheter-stent systems},
	volume = {37},
	year = {2009}}

@article{Skelton97,
	author = {Skelton, RP and Maier, HJ and Christ, H-J},
	date-added = {2021-06-28 07:15:40 -0400},
	date-modified = {2021-06-28 07:15:40 -0400},
	journal = {Materials Science and Engineering: A},
	number = {2},
	pages = {377--390},
	publisher = {Elsevier},
	title = {The Bauschinger effect, Masing model and the Ramberg--Osgood relation for cyclic deformation in metals},
	volume = {238},
	year = {1997}}

@article{Nims17,
	author = {Nims, Robert J and Ateshian, Gerard A},
	date-added = {2021-06-27 13:43:05 -0400},
	date-modified = {2021-06-27 13:43:05 -0400},
	journal = {Journal of Elasticity},
	number = {1-2},
	pages = {69--105},
	publisher = {Springer},
	title = {Reactive constrained mixtures for modeling the solid matrix of biological tissues},
	volume = {129},
	year = {2017}}

@article{Bonora97,
	author = {Bonora, Nicola},
	date-added = {2021-06-27 10:34:21 -0400},
	date-modified = {2021-06-27 10:34:21 -0400},
	journal = {Engineering fracture mechanics},
	number = {1-2},
	pages = {11--28},
	publisher = {Elsevier},
	title = {A nonlinear CDM model for ductile failure},
	volume = {58},
	year = {1997}}

@book{Lemaitre05,
	author = {Lemaitre, Jean and Desmorat, Rodrigue},
	date-added = {2021-06-27 10:33:56 -0400},
	date-modified = {2021-06-27 10:33:56 -0400},
	publisher = {Springer Science \& Business Media},
	title = {Engineering damage mechanics: ductile, creep, fatigue and brittle failures},
	year = {2005}}

@article{Zimmerman21,
	abstract = {This study presents a framework for plasticity and elastoplastic damage mechanics by treating materials as reactive solids whose internal composition evolves in response to applied loading. Using the framework of constrained reactive mixtures, plastic deformation is accounted for by allowing loaded bonds within the material to break and reform in a stressed state. Bonds which break and reform represent a new generation with a new reference configuration, which is time-invariant and provided by constitutive assumption. The constitutive relation for the reference configuration of each generation may depend on the selection of a suitable yield measure. The choice of this measure and the resulting plastic flow conditions are constrained by the Clausius-Duhem inequality. We show that this framework remains consistent with classical plasticity approaches and principles. Verification of this reactive plasticity framework, which is implemented in the open source FEBio finite element software (febio.org), is performed against standard 2D and 3D benchmark problems. Damage is incorporated into this reactive framework by allowing loaded bonds to break permanently according to a suitable damage measure, where broken bonds can no longer store free energy. Validation is also demonstrated against experimental data for problems involving plasticity and plastic damage. This study demonstrates that it is possible to formulate simple elastoplasticity and elastoplastic damage models within a consistent framework which uses measures of material mass composition as theoretically observable state variables. This theoretical frame can be expanded in scope to account for more complex behaviors.},
	author = {Brandon K. Zimmerman and David Jiang and Jeffrey A. Weiss and Lucas H. Timmins and Gerard A. Ateshian},
	date-added = {2021-06-27 10:31:23 -0400},
	date-modified = {2021-06-27 10:31:23 -0400},
	doi = {https://doi.org/10.1016/j.jmps.2021.104534},
	issn = {0022-5096},
	journal = {Journal of the Mechanics and Physics of Solids},
	keywords = {Reactive constrained mixtures, Continuum thermodynamics, Plasticity, Damage mechanics},
	pages = {104534},
	title = {On the use of constrained reactive mixtures of solids to model finite deformation isothermal elastoplasticity and elastoplastic damage mechanics},
	url = {https://www.sciencedirect.com/science/article/pii/S0022509621001940},
	year = {2021},
	Bdsk-Url-1 = {https://www.sciencedirect.com/science/article/pii/S0022509621001940},
	Bdsk-Url-2 = {https://doi.org/10.1016/j.jmps.2021.104534}}

@article{Papanastasiou87,
	author = {Papanastasiou, Tasos C},
	date-added = {2021-06-13 20:55:49 -0400},
	date-modified = {2021-06-13 20:56:02 -0400},
	journal = {Journal of Rheology},
	number = {5},
	pages = {385--404},
	publisher = {The Society of Rheology},
	title = {Flows of materials with yield},
	volume = {31},
	year = {1987}}

@article{Drucker49,
	author = {Drucker, Daniel Charles},
	date-added = {2021-05-16 18:26:09 -0400},
	date-modified = {2021-05-16 18:26:18 -0400},
	title = {Relation of experiments to mathematical theories of plasticity},
	year = {1949}}

@article{Hou89,
	abstract = {The objective of this study is to establish and verify the set of boundary conditions at the interface between a biphasic mixture (articular cartilage) and a Newtonian or non-Newtonian fluid (synovial fluid) such that a set of well-posed mathematical problems may be formulated to investigate joint lubrication problems. A "pseudo-no-slip" kinematic boundary condition is proposed based upon the principle that the conditions at the interface between mixtures or mixtures and fluids must reduce to those boundary conditions in single phase continuum mechanics. From this proposed kinematic boundary condition, and balances of mass, momentum and energy, the boundary conditions at the interface between a biphasic mixture and a Newtonian or non-Newtonian fluid are mathematically derived. Based upon these general results, the appropriate boundary conditions needed in modeling the cartilage-synovial fluid-cartilage lubrication problem are deduced. For two simple cases where a Newtonian viscous fluid is forced to flow (with imposed Couette or Poiseuille flow conditions) over a porous-permeable biphasic material of relatively low permeability, the well known empirical Taylor slip condition may be derived using matched asymptotic analysis of the boundary layer at the interface.},
	author = {Hou, J S and Holmes, M H and Lai, W M and Mow, V C},
	date-added = {2021-03-26 16:13:09 -0400},
	date-modified = {2021-03-26 16:13:09 -0400},
	doi = {10.1115/1.3168343},
	journal = {J Biomech Eng},
	journal-full = {Journal of biomechanical engineering},
	mesh = {Cartilage, Articular; Joints; Lubrication; Models, Biological; Rheology; Synovial Fluid; Viscosity},
	month = {Feb},
	number = {1},
	pages = {78-87},
	pmid = {2747237},
	pst = {ppublish},
	title = {Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications},
	volume = {111},
	year = {1989},
	Bdsk-Url-1 = {https://doi.org/10.1115/1.3168343}}

@article{Shim21a,
	author = {Shim, Jay J and Ateshian, Gerard A},
	date-added = {2021-03-26 16:03:44 -0400},
	date-modified = {2021-03-26 16:03:53 -0400},
	journal = {Archive of Applied Mechanics},
	pages = {1--21},
	publisher = {Springer},
	title = {A hybrid biphasic mixture formulation for modeling dynamics in porous deformable biological tissues},
	year = {2021}}

@article{Shim19,
	abstract = {Many physiological systems involve strong interactions between fluids and solids, posing a signicant challenge when modeling biomechanics. The objective of this study was to implement a fluid-structure interaction (FSI) solver in the free, open-source finite element code FEBio (febio.org), that combined the existing solid mechanics and rigid body dynamics solver with a recently-developed computational fluid dynamics (CFD) solver. A novel Galerkin-based finite element FSI formulation was introduced based on mixture theory, where the FSI domain was described as a mixture of fluid and solid constituents that have distinct motions. The mesh was defined on the solid domain, specialized to have zero mass, negligible stiffness and zero frictional interactions with the fluid, whereas the fluid was modeled as isothermal and compressible. The mixture framework provided the foundation for evaluating material time derivatives in a material frame for the solid and in a spatial frame for the fluid. Similar to our recently reported CFD solver, our FSI formulation did not require stabilization methods to achieve good convergence, producing a compact set of equations and code implementation. The code was successfully verified against benchmark problems and an analytical solution for squeeze-film lubrication. It was validated against experimental measurements of the flow rate in a peristaltic pump, and illustrated using non-Newtonian blood flow through a bifurcated carotid artery with a thick arterial wall. The successful formulation and implementation of this FSI solver enhances the multiphysics modeling capabilities in FEBio relevant to the biomechanics and biophysics communities.},
	author = {Shim, Jay J and Maas, Steve A and Weiss, Jeffrey A and Ateshian, Gerard A},
	date-added = {2021-03-26 16:02:30 -0400},
	date-modified = {2021-03-26 16:02:30 -0400},
	doi = {10.1115/1.4043031},
	journal = {J Biomech Eng},
	journal-full = {Journal of biomechanical engineering},
	month = {Mar},
	pmc = {PMC6528685},
	pmid = {30835271},
	pst = {aheadofprint},
	title = {A Formulation for Fluid Structure-Interactions in FEBio Using Mixture Theory},
	year = {2019},
	Bdsk-Url-1 = {https://doi.org/10.1115/1.4043031}}

@article{Gatti20,
	abstract = {Pulse wave imaging (PWI) is an ultrasound-based method that allows spatiotemporal mapping of the arterial pulse wave propagation, from which the local pulse wave velocity (PWV) can be derived. Recent reports indicate that PWI can help the assessment of atherosclerotic plaque composition and mechanical properties. However, the effect of the atherosclerotic plaque's geometry and mechanics on the arterial wall distension and local PWV remains unclear. In this study we investigated the accuracy of a finite element (FE) fluid-structure interaction (FSI) approach to predict the velocity of a pulse wave propagating through a stenotic artery with an asymmetrical plaque, as quantified with PWI method. Experiments were designed to compare FE-FSI modeling of the pulse wave propagation through a stenotic artery against PWI obtained with manufactured phantom arteries made of PVA material. FSI-generated spatiotemporal maps were used to estimate PWV at the plaque region and compare it to the experimental results. Velocity of the pulse wave propagation and magnitude of the wall distension were correctly predicted with the FE analysis. In addition, findings indicate that a plaque with a high degree of stenosis (>70%) attenuates the propagation of the pulse pressure wave. Results of this study support the validity of the FE-FSI methods to investigate the effect of arterial wall structural and mechanical properties on the pulse wave propagation. This modeling method can help to guide the optimization of PWI to characterize plaque properties and substantiate clinical findings.},
	author = {Gatti, Vittorio and Nauleau, Pierre and Karageorgos, Grigorios Mario and Shim, Jay J and Ateshian, Gerard A and Konofagou, Elisa E},
	date-added = {2021-03-26 16:02:27 -0400},
	date-modified = {2021-03-26 16:02:27 -0400},
	doi = {10.1115/1.4048708},
	journal = {J Biomech Eng},
	journal-full = {Journal of biomechanical engineering},
	month = {Oct},
	pmc = {PMC7872000},
	pmid = {33030208},
	pst = {aheadofprint},
	title = {Modelling Pulse Wave Propagation Through a Stenotic Artery with Fluid Structure Interaction: A Validation Study Using Ultrasound Pulse Wave Imaging},
	year = {2020},
	Bdsk-Url-1 = {https://doi.org/10.1115/1.4048708}}

@article{Shim21,
	abstract = {In biomechanics, solid-fluid mixtures have commonly been used to model the response of hydrated biological tissues. In cartilage mechanics, this type of mixture, where the fluid and solid constituents are both assumed to be intrinsically incompressible, is often called a biphasic material. Various physiological processes involve the interaction of a viscous fluid with a porous-hydrated tissue, as encountered in synovial joint lubrication, cardiovascular mechanics, and respiratory mechanics. The objective of this study was to implement a finite element solver in the open-source software FEBio that models dynamic interactions between a viscous fluid and a biphasic domain, accommodating finite deformations of both domains as well as fluid exchanges between them. For compatibility with our recent implementation of solvers for computational fluid dynamics (CFD) and fluid-structure interactions (FSI), where the fluid is slightly compressible, this study employs a novel hybrid biphasic formulation where the porous skeleton is intrinsically incompressible but the fluid is also slightly compressible. The resulting biphasic-FSI (BFSI) implementation is verified against published analytical and numerical benchmark problems, as well as novel analytical solutions derived for the purposes of this study. An illustration of this BFSI solver is presented for two-dimensional air flow through a simulated face mask under five cycles of breathing, showing that masks significantly reduce air dispersion compared to the no-mask control analysis. The successful formulation and implementation of this BFSI solver offers enhanced multiphysics modeling capabilities that are accessible via an open-source software platform.},
	author = {Shim, Jay J and Maas, Steve A and Weiss, Jeffrey A and Ateshian, Gerard A},
	date-added = {2021-03-26 16:02:25 -0400},
	date-modified = {2021-03-26 16:02:25 -0400},
	doi = {10.1115/1.4050646},
	journal = {J Biomech Eng},
	journal-full = {Journal of biomechanical engineering},
	month = {Mar},
	pmid = {33764435},
	pst = {aheadofprint},
	title = {Finite Element Implementation of Biphasic-Fluid Structure Interactions in FEBio},
	year = {2021},
	Bdsk-Url-1 = {https://doi.org/10.1115/1.4050646}}

@article{Gultekin19,
	author = {G{\"u}ltekin, Osman and Dal, H{\"u}sn{\"u} and Holzapfel, Gerhard A},
	date-added = {2020-12-23 09:12:27 -0500},
	date-modified = {2020-12-23 09:12:37 -0500},
	journal = {Computational mechanics},
	number = {3},
	pages = {443--453},
	publisher = {Springer},
	title = {On the quasi-incompressible finite element analysis of anisotropic hyperelastic materials},
	volume = {63},
	year = {2019}}

@article{Sansour08,
	author = {Sansour, Carlo},
	date-added = {2020-12-23 09:11:29 -0500},
	date-modified = {2020-12-23 09:12:32 -0500},
	journal = {European Journal of Mechanics-A/Solids},
	number = {1},
	pages = {28--39},
	publisher = {Elsevier},
	title = {On the physical assumptions underlying the volumetric-isochoric split and the case of anisotropy},
	volume = {27},
	year = {2008}}

@article{Helfenstein10,
	author = {Helfenstein, J and Jabareen, M and Mazza, Edoardo and Govindjee, S},
	date-added = {2020-12-23 08:58:40 -0500},
	date-modified = {2020-12-23 08:58:46 -0500},
	journal = {International Journal of Solids and Structures},
	number = {16},
	pages = {2056--2061},
	publisher = {Elsevier},
	title = {On non-physical response in models for fiber-reinforced hyperelastic materials},
	volume = {47},
	year = {2010}}

@article{Simo87a,
	author = {Simo, Juan C and Ju, JW},
	date-added = {2020-08-23 18:43:17 -0400},
	date-modified = {2020-08-23 18:44:13 -0400},
	journal = {International journal of solids and structures},
	number = {7},
	pages = {821--840},
	publisher = {Elsevier},
	title = {Strain-and stress-based continuum damage models---I. Formulation},
	volume = {23},
	year = {1987}}

@article{Chaboche81,
	author = {Chaboche, Jean-Louis},
	date-added = {2020-08-23 18:42:58 -0400},
	date-modified = {2020-08-23 18:43:23 -0400},
	journal = {Nuclear Engineering and Design},
	number = {2},
	pages = {233--247},
	publisher = {Elsevier},
	title = {Continuous damage mechanics---a tool to describe phenomena before crack initiation},
	volume = {64},
	year = {1981}}

@article{Lemaitre85,
	author = {Lemaitre, Jean},
	date-added = {2020-08-23 18:42:37 -0400},
	date-modified = {2020-08-23 18:43:33 -0400},
	journal = {J. Eng. Mater. Technol.},
	title = {A continuous damage mechanics model for ductile fracture},
	year = {1985}}

@article{Lemaitre84,
	author = {Lemaitre, Jean},
	date-added = {2020-08-23 18:42:20 -0400},
	date-modified = {2020-08-23 18:43:31 -0400},
	journal = {Nuclear engineering and design},
	number = {2},
	pages = {233--245},
	publisher = {Elsevier},
	title = {How to use damage mechanics},
	volume = {80},
	year = {1984}}

@book{Rabotnov80,
	author = {Rabotnov, Yu N},
	date-added = {2020-08-23 18:41:17 -0400},
	date-modified = {2020-08-23 18:45:19 -0400},
	publisher = {MIT Publishers, Moscow},
	title = {Elements of hereditary solid mechanics},
	year = {1980}}

@article{Kachanov58,
	author = {Kachanov, Lazar M},
	date-added = {2020-08-23 18:40:55 -0400},
	date-modified = {2020-08-23 18:44:51 -0400},
	journal = {International Journal of Fracture},
	publisher = {IZVESTIA ACADEMII NAUK SSSR OTDELENIE TEKHNICHESKICH NAUK},
	title = {Rupture time under creep conditions},
	year = {1958}}

@article{Nims16,
	abstract = {This study presents a damage mechanics framework that employs observable state variables to describe damage in isotropic or anisotropic fibrous tissues. In this mixture theory framework, damage is tracked by the mass fraction of bonds that have broken. Anisotropic damage is subsumed in the assumption that multiple bond species may coexist in a material, each having its own damage behaviour. This approach recovers the classical damage mechanics formulation for isotropic materials, but does not appeal to a tensorial damage measure for anisotropic materials. In contrast with the classical approach, the use of observable state variables for damage allows direct comparison of model predictions to experimental damage measures, such as biochemical assays or Raman spectroscopy. Investigations of damage in discrete fibre distributions demonstrate that the resilience to damage increases with the number of fibre bundles; idealizing fibrous tissues using continuous fibre distribution models precludes the modelling of damage. This damage framework was used to test and validate the hypothesis that growth of cartilage constructs can lead to damage of the synthesized collagen matrix due to excessive swelling caused by synthesized glycosaminoglycans. Therefore, alternative strategies must be implemented in tissue engineering studies to prevent collagen damage during the growth process. },
	author = {Nims, Robert J and Durney, Krista M and Cigan, Alexander D and Duss{\'e}aux, Antoine and Hung, Clark T and Ateshian, Gerard A},
	date-added = {2020-08-23 18:21:23 -0400},
	date-modified = {2020-08-23 18:21:32 -0400},
	doi = {10.1098/rsfs.2015.0063},
	journal = {Interface Focus},
	journal-full = {Interface focus},
	keywords = {cartilage tissue engineering; damage mechanics; fibrous tissues},
	month = {Feb},
	number = {1},
	pages = {20150063},
	pmc = {PMC4686240},
	pmid = {26855751},
	pst = {ppublish},
	title = {Continuum theory of fibrous tissue damage mechanics using bond kinetics: application to cartilage tissue engineering},
	volume = {6},
	year = {2016},
	Bdsk-Url-1 = {https://doi.org/10.1098/rsfs.2015.0063}}

@article{Hou18,
	author = {Hou, Jay C and Maas, Steve A and Weiss, Jeffrey A and Ateshian, Gerard A},
	date-added = {2020-07-30 18:51:23 -0400},
	date-modified = {2020-07-30 18:51:34 -0400},
	journal = {Journal of Biomechanical Engineering},
	number = {12},
	publisher = {American Society of Mechanical Engineers Digital Collection},
	title = {Finite Element Formulation of Multiphasic Shell Elements for Cell Mechanics Analyses in FEBio},
	volume = {140},
	year = {2018}}

@article{Simo93,
	author = {Simo, JC and Armero, F and Taylor, RL},
	date-added = {2020-07-30 17:19:55 -0400},
	date-modified = {2020-07-30 17:20:02 -0400},
	journal = {Computer methods in applied mechanics and engineering},
	number = {3-4},
	pages = {359--386},
	publisher = {Elsevier},
	title = {Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems},
	volume = {110},
	year = {1993}}

@article{Simo90,
	author = {Simo, Juan C and Rifai, MS10587420724},
	date-added = {2020-07-30 17:18:41 -0400},
	date-modified = {2020-07-30 17:18:55 -0400},
	journal = {International journal for numerical methods in engineering},
	number = {8},
	pages = {1595--1638},
	publisher = {Wiley Online Library},
	title = {A class of mixed assumed strain methods and the method of incompatible modes},
	volume = {29},
	year = {1990}}

@article{Vu-Quoc03,
	author = {Vu-Quoc, L and Tan, XG},
	date-added = {2020-07-30 17:16:13 -0400},
	date-modified = {2020-07-30 17:16:31 -0400},
	journal = {Computer methods in applied mechanics and engineering},
	number = {9-10},
	pages = {975--1016},
	publisher = {Elsevier},
	title = {Optimal solid shells for non-linear analyses of multilayer composites. I. Statics},
	volume = {192},
	year = {2003}}

@article{Klinkel99,
	author = {Klinkel, S and Gruttmann, F and Wagner, W},
	date-added = {2020-07-30 17:15:51 -0400},
	date-modified = {2020-07-30 17:16:25 -0400},
	journal = {Computers \& Structures},
	number = {1},
	pages = {43--62},
	publisher = {Elsevier},
	title = {A continuum based three-dimensional shell element for laminated structures},
	volume = {71},
	year = {1999}}

@article{Bischoff97,
	author = {Bischoff, M and Ramm, E},
	date-added = {2020-07-30 17:15:20 -0400},
	date-modified = {2020-07-30 17:15:29 -0400},
	journal = {International Journal for Numerical Methods in Engineering},
	number = {23},
	pages = {4427--4449},
	publisher = {Wiley Online Library},
	title = {Shear deformable shell elements for large strains and rotations},
	volume = {40},
	year = {1997}}

@article{Betsch95,
	author = {Betsch, P and Stein, E},
	date-added = {2020-07-30 17:14:57 -0400},
	date-modified = {2020-07-30 17:15:04 -0400},
	journal = {Communications in Numerical Methods in Engineering},
	number = {11},
	pages = {899--909},
	publisher = {Wiley Online Library},
	title = {An assumed strain approach avoiding artificial thickness straining for a non-linear 4-node shell element},
	volume = {11},
	year = {1995}}

@article{Bathe86,
	author = {Bathe, Klaus-J{\"u}rgen and Dvorkin, Eduardo N},
	date-added = {2020-07-30 17:14:19 -0400},
	date-modified = {2020-07-30 17:14:24 -0400},
	journal = {International journal for numerical methods in engineering},
	number = {3},
	pages = {697--722},
	publisher = {Wiley Online Library},
	title = {A formulation of general shell elements---the use of mixed interpolation of tensorial components},
	volume = {22},
	year = {1986}}

@article{MacNeal78,
	author = {MacNeal, Richard H},
	date-added = {2020-07-30 17:13:45 -0400},
	date-modified = {2020-07-30 17:13:55 -0400},
	journal = {Computers \& Structures},
	number = {2},
	pages = {175--183},
	publisher = {Elsevier},
	title = {A simple quadrilateral shell element},
	volume = {8},
	year = {1978}}

@article{Bischoff18,
	author = {Bischoff, Manfred and Ramm, E and Irslinger, J},
	date-added = {2020-07-30 17:12:54 -0400},
	date-modified = {2020-07-30 17:13:05 -0400},
	journal = {Encyclopedia of Computational Mechanics Second Edition},
	pages = {1--86},
	publisher = {Wiley Online Library},
	title = {Models and finite elements for thin-walled structures},
	year = {2018}}

@article{Gasser06,
	abstract = {Constitutive relations are fundamental to the solution of problems in continuum mechanics, and are required in the study of, for example, mechanically dominated clinical interventions involving soft biological tissues. Structural continuum constitutive models of arterial layers integrate information about the tissue morphology and therefore allow investigation of the interrelation between structure and function in response to mechanical loading. Collagen fibres are key ingredients in the structure of arteries. In the media (the middle layer of the artery wall) they are arranged in two helically distributed families with a small pitch and very little dispersion in their orientation (i.e. they are aligned quite close to the circumferential direction). By contrast, in the adventitial and intimal layers, the orientation of the collagen fibres is dispersed, as shown by polarized light microscopy of stained arterial tissue. As a result, continuum models that do not account for the dispersion are not able to capture accurately the stress-strain response of these layers. The purpose of this paper, therefore, is to develop a structural continuum framework that is able to represent the dispersion of the collagen fibre orientation. This then allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls, and is a generalization of the fibre-reinforced structural model introduced by Holzapfel & Gasser (Holzapfel & Gasser 2001 Comput. Meth. Appl. Mech. Eng. 190, 4379-4403) and Holzapfel et al. (Holzapfel et al. 2000 J. Elast. 61, 1-48). The model incorporates an additional scalar structure parameter that characterizes the dispersed collagen orientation. An efficient finite element implementation of the model is then presented and numerical examples show that the dispersion of the orientation of collagen fibres in the adventitia of human iliac arteries has a significant effect on their mechanical response.},
	author = {Gasser, T Christian and Ogden, Ray W and Holzapfel, Gerhard A},
	date-added = {2020-02-27 09:16:38 -0500},
	date-modified = {2020-02-27 09:16:38 -0500},
	doi = {10.1098/rsif.2005.0073},
	journal = {J R Soc Interface},
	journal-full = {Journal of the Royal Society, Interface},
	mesh = {Animals; Anisotropy; Arteries; Biomechanical Phenomena; Elasticity; Fibrillar Collagens; Humans; Models, Cardiovascular; Protein Conformation; Stress, Mechanical},
	month = {Feb},
	number = {6},
	pages = {15-35},
	pmc = {PMC1618483},
	pmid = {16849214},
	pst = {ppublish},
	title = {Hyperelastic modelling of arterial layers with distributed collagen fibre orientations},
	volume = {3},
	year = {2006},
	Bdsk-Url-1 = {https://doi.org/10.1098/rsif.2005.0073}}

@article{Criscione00,
	author = {Criscione, John C and Humphrey, Jay D and Douglas, Andrew S and Hunter, William C},
	date-added = {2019-09-07 09:58:47 -0400},
	date-modified = {2019-09-07 09:59:18 -0400},
	journal = {J. Mech. Phys. Solids},
	number = {12},
	pages = {2445--2465},
	publisher = {Elsevier},
	title = {An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity},
	volume = {48},
	year = {2000}}

@article{Ateshian18,
	abstract = {The mechanics of biological fluids is an important topic in biomechanics, often requiring the use of computational tools to analyze problems with realistic geometries and material properties. This study describes the formulation and implementation of a finite element framework for computational fluid dynamics (CFD) in FEBio, a free software designed to meet the computational needs of the biomechanics and biophysics communities. This formulation models nearly incompressible flow with a compressible isothermal formulation that uses a physically realistic value for the fluid bulk modulus. It employs fluid velocity and dilatation as essential variables: The virtual work integral enforces the balance of linear momentum and the kinematic constraint between fluid velocity and dilatation, while fluid density varies with dilatation as prescribed by the axiom of mass balance. Using this approach, equal-order interpolations may be used for both essential variables over each element, contrary to traditional mixed formulations that must explicitly satisfy the inf-sup condition. The formulation accommodates Newtonian and non-Newtonian viscous responses as well as inviscid fluids. The efficiency of numerical solutions is enhanced using Broyden's quasi-Newton method. The results of finite element simulations were verified using well-documented benchmark problems as well as comparisons with other free and commercial codes. These analyses demonstrated that the novel formulation introduced in FEBio could successfully reproduce the results of other codes. The analogy between this CFD formulation and standard finite element formulations for solid mechanics makes it suitable for future extension to fluid-structure interactions (FSIs).},
	author = {Ateshian, Gerard A and Shim, Jay J and Maas, Steve A and Weiss, Jeffrey A},
	date-added = {2018-08-05 11:55:36 -0400},
	date-modified = {2018-08-05 11:55:36 -0400},
	doi = {10.1115/1.4038716},
	journal = {J Biomech Eng},
	journal-full = {Journal of biomechanical engineering},
	month = {Feb},
	number = {2},
	pmc = {PMC5816258},
	pmid = {29238817},
	pst = {ppublish},
	title = {Finite Element Framework for Computational Fluid Dynamics in FEBio},
	volume = {140},
	year = {2018},
	Bdsk-Url-1 = {https://doi.org/10.1115/1.4038716}}

@article{Bazilevs08,
	author = {Bazilevs, Yuri and Calo, Victor M and Hughes, Thomas JR and Zhang, Yongjie},
	date-added = {2018-03-11 22:10:43 +0000},
	date-modified = {2018-03-11 22:10:50 +0000},
	journal = {Computational mechanics},
	number = {1},
	pages = {3--37},
	publisher = {Springer},
	title = {Isogeometric fluid-structure interaction: theory, algorithms, and computations},
	volume = {43},
	year = {2008}}

@article{Simo91a,
	author = {Simo, Juan Carlos and Wong, Kachung Kevin},
	date-added = {2017-05-17 11:32:46 +0000},
	date-modified = {2017-05-17 11:32:55 +0000},
	journal = {International journal for numerical methods in engineering},
	number = {1},
	pages = {19--52},
	publisher = {Wiley Online Library},
	title = {Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum},
	volume = {31},
	year = {1991}}

@article{Puso02,
	author = {Puso, Michael Anthony},
	date-added = {2017-05-17 11:29:50 +0000},
	date-modified = {2017-05-17 11:30:01 +0000},
	journal = {International Journal for numerical methods in engineering},
	number = {6},
	pages = {1393--1414},
	publisher = {Wiley Online Library},
	title = {An energy and momentum conserving method for rigid--flexible body dynamics},
	volume = {53},
	year = {2002}}

@article{Gonzalez00,
	author = {Gonzalez, Oscar},
	date-added = {2017-05-17 11:29:12 +0000},
	date-modified = {2017-05-17 11:29:18 +0000},
	journal = {Computer Methods in Applied Mechanics and Engineering},
	number = {13},
	pages = {1763--1783},
	publisher = {Elsevier},
	title = {Exact energy and momentum conserving algorithms for general models in nonlinear elasticity},
	volume = {190},
	year = {2000}}

@article{Simo92b,
	author = {Simo, Juan C and Tarnow, N and Wong, KK},
	date-added = {2017-05-17 11:28:15 +0000},
	date-modified = {2017-05-17 11:28:30 +0000},
	journal = {Computer methods in applied mechanics and engineering},
	number = {1},
	pages = {63--116},
	publisher = {Elsevier},
	title = {Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics},
	volume = {100},
	year = {1992}}

@article{Simo92a,
	author = {Simo, JC and Tarnow, Nils},
	date-added = {2017-05-17 11:28:00 +0000},
	date-modified = {2017-05-17 11:28:27 +0000},
	journal = {Zeitschrift f{\"u}r angewandte Mathematik und Physik (ZAMP)},
	number = {5},
	pages = {757--792},
	publisher = {Springer},
	title = {The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics},
	volume = {43},
	year = {1992}}

@article{Hilber77,
	author = {Hilber, Hans M and Hughes, Thomas JR and Taylor, Robert L},
	date-added = {2017-05-17 11:26:42 +0000},
	date-modified = {2017-05-17 11:26:49 +0000},
	journal = {Earthquake Engineering \&amp; Structural Dynamics},
	number = {3},
	pages = {283--292},
	publisher = {Wiley Online Library},
	title = {Improved numerical dissipation for time integration algorithms in structural dynamics},
	volume = {5},
	year = {1977}}

@article{Vignon-Clementel06,
	author = {Vignon-Clementel, Irene E and Figueroa, C Alberto and Jansen, Kenneth E and Taylor, Charles A},
	date-added = {2017-05-17 00:38:10 +0000},
	date-modified = {2017-05-17 00:38:10 +0000},
	journal = {Comput. Methods Appl. Mech. Engrg.},
	journal-full = {Computer methods in applied mechanics and engineering},
	number = {29},
	pages = {3776--3796},
	publisher = {Elsevier},
	title = {Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries},
	volume = {195},
	year = {2006}}

@article{Esmaily-Moghadam11,
	author = {Esmaily Moghadam, Mahdi and Bazilevs, Yuri and Hsia, Tain-Yen and Vignon-Clementel, Irene E and Marsden, Alison L},
	date-added = {2017-05-17 00:37:42 +0000},
	date-modified = {2017-05-17 00:37:42 +0000},
	journal = {Comput. Mech.},
	journal-full = {Computational Mechanics},
	number = {3},
	pages = {277--291},
	publisher = {Springer},
	title = {A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations},
	volume = {48},
	year = {2011}}

@article{Bazilevs09,
	author = {Bazilevs, Y and Gohean, JR and Hughes, TJR and Moser, RD and Zhang, Y},
	date-added = {2017-05-17 00:37:37 +0000},
	date-modified = {2017-05-17 00:37:37 +0000},
	journal = {Comput. Methods Appl. Mech. Engrg.},
	journal-full = {Computer Methods in Applied Mechanics and Engineering},
	number = {45},
	pages = {3534--3550},
	publisher = {Elsevier},
	title = {Patient-specific isogeometric fluid--structure interaction analysis of thoracic aortic blood flow due to implantation of the {Jarvik} 2000 left ventricular assist device},
	volume = {198},
	year = {2009}}

@book{Reddy01,
	address = {Boca Raton, FL},
	author = {Reddy, J. N. and Gartling, David K.},
	date-added = {2017-05-17 00:36:56 +0000},
	date-modified = {2017-05-17 00:36:56 +0000},
	edition = {2nd},
	isbn = {084932355X (alk. paper)},
	pages = {469 p.},
	publisher = {CRC Press},
	title = {The finite element method in heat transfer and fluid dynamics},
	type = {Book},
	url = {Publisher description http://www.loc.gov/catdir/enhancements/fy0646/00048638-d.html},
	year = {2001},
	Bdsk-Url-1 = {Publisher%20description%20http://www.loc.gov/catdir/enhancements/fy0646/00048638-d.html}}

@article{Cho91,
	abstract = {Effects of the non-Newtonian viscosity of blood on a flow in a coronary arterial casting of man were studied numerically using a finite element method. Various constitutive models were examined to model the non-Newtonian viscosity of blood and their model constants were summarized. A method to incorporate the non-Newtonian viscosity of blood was introduced so that the viscosity could be calculated locally. The pressure drop, wall shear stress and velocity profiles for the case of blood viscosity were compared for the case of Newtonian viscosity (0.0345 poise). The effect of the non-Newtonian viscosity of blood on the overall pressure drop across the arterial casting was found to be significant at a flow of the Reynolds number of 100 or less. Also in the region of flow separation or recirculation, the non-Newtonian viscosity of blood yields larger wall shear stress than the Newtonian case. The origin of the non-Newtonian viscosity of blood was discussed in relation to the viscoelasticity and yield stress of blood.},
	author = {Cho, Y I and Kensey, K R},
	date-added = {2017-05-17 00:24:02 +0000},
	date-modified = {2017-05-17 00:24:02 +0000},
	journal = {Biorheology},
	journal-full = {Biorheology},
	mesh = {Biomechanical Phenomena; Blood Pressure; Blood Viscosity; Coronary Disease; Coronary Vessels; Humans; Models, Biological; Regional Blood Flow},
	number = {3-4},
	pages = {241-62},
	pmid = {1932716},
	pst = {ppublish},
	title = {Effects of the non-{Newtonian} viscosity of blood on flows in a diseased arterial vessel. {Part} 1: {Steady} flows},
	volume = {28},
	year = {1991}}

@book{Panton06,
	author = {Panton, Ronald L},
	date-added = {2017-05-17 00:23:49 +0000},
	date-modified = {2017-05-17 00:23:49 +0000},
	publisher = {John Wiley \&amp; Sons},
	title = {Incompressible flow},
	year = {2006}}

@book{Reddy08,
	address = {New York},
	author = {Reddy, J. N.},
	date-added = {2017-05-17 00:23:33 +0000},
	date-modified = {2017-05-17 00:23:33 +0000},
	isbn = {9780521870443 (hardback) 0521870445 (hardback)},
	pages = {xiv, 354 p.},
	publisher = {Cambridge University Press},
	title = {An introduction to continuum mechanics : with applications},
	type = {Book},
	url = {Table of contents only http://www.loc.gov/catdir/toc/ecip0720/2007025254.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0729/2007025254-b.html Publisher description http://www.loc.gov/catdir/enhancements/fy0729/2007025254-d.html},
	year = {2008},
	Bdsk-Url-1 = {Table%20of%20contents%20only%20http://www.loc.gov/catdir/toc/ecip0720/2007025254.html%20Contributor%20biographical%20information%20http://www.loc.gov/catdir/enhancements/fy0729/2007025254-b.html%20Publisher%20description%20http://www.loc.gov/catdir/enhancements/fy0729/2007025254-d.html}}

@article{Jansen00,
	author = {Jansen, Kenneth E and Whiting, Christian H and Hulbert, Gregory M},
	date-added = {2017-05-17 00:20:46 +0000},
	date-modified = {2017-05-17 00:20:46 +0000},
	journal = {Comput. Methods Appl. Mech. Engrg.},
	journal-full = {Computer Methods in Applied Mechanics and Engineering},
	number = {3},
	pages = {305--319},
	publisher = {Elsevier},
	title = {A generalized-$\alpha$ method for integrating the filtered {Navier}--{Stokes} equations with a stabilized finite element method},
	volume = {190},
	year = {2000}}

@article{Ateshian12,
	abstract = {A finite element formulation of neutral solute transport across a contact interface between deformable porous media is implemented and validated against analytical solutions. By reducing the integral statements of external virtual work on the two contacting surfaces into a single contact integral, the algorithm automatically enforces continuity of solute molar flux across the contact interface, whereas continuity of the effective solute concentration (a measure of the solute mechano-chemical potential) is achieved using a penalty method. This novel formulation facilitates the analysis of problems in biomechanics where the transport of metabolites across contact interfaces of deformable tissues may be of interest. This contact algorithm is the first to address solute transport across deformable interfaces, and is made available in the public domain, open-source finite element code FEBio (http://www.febio.org).},
	author = {Ateshian, Gerard A and Maas, Steve and Weiss, Jeffrey A},
	date-added = {2017-01-22 16:40:27 +0000},
	date-modified = {2017-01-22 16:40:27 +0000},
	doi = {10.1016/j.jbiomech.2012.01.003},
	journal = {J Biomech},
	journal-full = {Journal of biomechanics},
	mesh = {Algorithms; Animals; Biological Transport; Finite Element Analysis; Humans; Models, Biological; Porosity},
	month = {Apr},
	number = {6},
	pages = {1023-7},
	pmc = {PMC3351088},
	pmid = {22281406},
	pst = {ppublish},
	title = {Solute transport across a contact interface in deformable porous media},
	volume = {45},
	year = {2012},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jbiomech.2012.01.003}}

@book{Bathe82,
	address = {Englewood Cliffs, N.J.},
	annote = {LDR    00952pam  2200265 a 4500
001    2787910
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082 00 $a620/.00422$219
100 1  $aBathe, Klaus-J{\"u}rgen.
245 10 $aFinite element procedures in engineering analysis /$cKlaus-J{\"u}rgen Bathe.
260    $aEnglewood Cliffs, N.J. :$bPrentice-Hall,$cc1982.
300    $axiii, 735 p. :$bill. ;$c24 cm.
440  0 $aPrentice-Hall civil engineering and engineering mechanics series
504    $aIncludes bibliographical references and index.
650  0 $aFinite element method.
650  0 $aEngineering mathematics.
991    $bc-GenColl$hTA347.F5$iB36$p00009571851$tCopy 1$wBOOKS
},
	author = {Bathe, Klaus-J{\"u}rgen},
	call-number = {TA347.F5},
	date-added = {2016-12-27 19:16:12 +0000},
	date-modified = {2016-12-27 19:16:12 +0000},
	dewey-call-number = {620/.00422},
	genre = {Finite element method},
	isbn = {0133173054},
	library-id = {81012067},
	publisher = {Prentice-Hall},
	title = {Finite element procedures in engineering analysis},
	year = {1982}}

@article{Azeloglu08,
	abstract = {The arterial wall contains a significant amount of charged proteoglycans, which are inhomogeneously distributed, with the greatest concentrations in the intimal and medial layers. The hypothesis of this study is that the transmural distribution of proteoglycans plays a significant role in regulating residual stresses in the arterial wall. This hypothesis was first tested theoretically, using the framework of mixture theory for charged hydrated tissues, and then verified experimentally by measuring the opening angle of rat aorta in NaCl solutions of various ionic strengths. A three-dimensional finite element model of aortic ring, using realistic values of the solid matrix shear modulus and proteoglycan fixed-charge density, yielded opening angles and changes with osmolarity comparable to values reported in the literature. Experimentally, the mean opening angle in isotonic saline (300 mosM) was 15 +/- 17 degrees and changed to 4 +/- 19 degrees and 73 +/- 18 degrees under hypertonic (2,000 mosM) and hypotonic (0 mosM) conditions, respectively (n = 16). In addition, the opening angle in isotonic (300 mosM) sucrose, an uncharged molecule, was 60 +/- 16 degrees (n = 11), suggesting that the charge effect, not cellular swelling, was the major underlying mechanism for these observations. The extent of changes in opening angle under osmotic challenges suggests that transmural heterogeneity of fixed-charge density plays a crucial role in governing the zero-stress configuration of the aorta. A significant implication of this finding is that arterial wall remodeling in response to altered wall stresses may occur via altered deposition of proteoglycans across the wall thickness, providing a novel mechanism for regulating mechanical homeostasis in vascular tissue.},
	author = {Azeloglu, Evren U and Albro, Michael B and Thimmappa, Vikrum A and Ateshian, Gerard A and Costa, Kevin D},
	date-added = {2016-12-27 19:05:22 +0000},
	date-modified = {2016-12-27 19:05:22 +0000},
	doi = {10.1152/ajpheart.01027.2007},
	journal = {Am J Physiol Heart Circ Physiol},
	journal-full = {American journal of physiology. Heart and circulatory physiology},
	mesh = {Algorithms; Animals; Aorta, Thoracic; Finite Element Analysis; Glycosaminoglycans; In Vitro Techniques; Male; Osmolar Concentration; Poisson Distribution; Proteoglycans; Rats; Rats, Sprague-Dawley; Stress, Physiological},
	month = {Mar},
	number = {3},
	pages = {H1197-205},
	pmid = {18156194},
	pst = {ppublish},
	title = {Heterogeneous transmural proteoglycan distribution provides a mechanism for regulating residual stresses in the aorta},
	volume = {294},
	year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1152/ajpheart.01027.2007}}

@book{Holzapfel00,
	address = {Chichester},
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100 1  $aHolzapfel, Gerhard A.
245 10 $aNonlinear solid mechanics :$ba continuum approach for engineering /$cGerhard A. Holzapfel.
260    $aChichester ;$aNew York :$bWiley,$cc2000.
300    $axiv, 455 p. :$bill. ;$c25 cm.
504    $aIncludes bibliographical references (p. 415-433) and index.
650  0 $aContinuum mechanics.
856 42 $3Publisher description$uhttp://www.loc.gov/catdir/description/wiley035/00027315.html
856 4  $3Table of Contents$uhttp://www.loc.gov/catdir/toc/onix06/00027315.html
},
	author = {Holzapfel, Gerhard A},
	call-number = {QA808.2},
	date-added = {2016-12-27 18:45:16 +0000},
	date-modified = {2016-12-27 18:45:16 +0000},
	dewey-call-number = {531},
	genre = {Continuum mechanics},
	isbn = {047182304X (acid-free paper)},
	library-id = {00027315},
	publisher = {Wiley},
	title = {Nonlinear solid mechanics: a continuum approach for engineering},
	url = {http://www.loc.gov/catdir/description/wiley035/00027315.html},
	year = {2000},
	Bdsk-Url-1 = {http://www.loc.gov/catdir/description/wiley035/00027315.html}}

@book{Lai10,
	address = {Amsterdam},
	annote = {LDR    01115cam  2200289 a 4500
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050 00 $aQA808.2$b.L3 2010
082 00 $a531$222
100 1  $aLai, W. Michael,$d1930-
245 10 $aIntroduction to continuum mechanics /$cW. Michael Lai, David Rubin, Erhard Krempl.
250    $a4th ed.
260    $aAmsterdam ;$aBoston :$bButterworth-Heinemann/Elsevier,$cc2010.
300    $axiv, 520 p. :$bill. ;$c25 cm.
504    $aIncludes bibliographical references and index.
650  0 $aContinuum mechanics.
700 1  $aRubin, David,$d1942-
700 1  $aKrempl, Erhard.
},
	author = {Lai, W. Michael and Rubin, David and Krempl, Erhard},
	call-number = {QA808.2},
	date-added = {2016-12-27 18:43:23 +0000},
	date-modified = {2016-12-27 18:43:23 +0000},
	dewey-call-number = {531},
	edition = {4th ed},
	genre = {Continuum mechanics},
	isbn = {9780750685603 (hardcover)},
	library-id = {2009003607},
	publisher = {Butterworth-Heinemann/Elsevier},
	title = {Introduction to continuum mechanics},
	year = {2010}}

@article{Weinans92,
	abstract = {The process of adaptive bone remodeling can be described mathematically and simulated in a computer model, integrated with the finite element method. In the model discussed here, cortical and trabecular bone are described as continuous materials with variable density. The remodeling rule applied to simulate the remodeling process in each element individually is, in fact, an objective function for an optimization process, relative to the external load. Its purpose is to obtain a constant, preset value for the strain energy per unit bone mass, by adapting the density. If an element in the structure cannot achieve that, it either turns to its maximal density (cortical bone) or resorbs completely. It is found that the solution obtained in generally a discontinuous patchwork. For a two-dimensional proximal femur model this patchwork shows a good resemblance with the density distribution of a real proximal femur. It is shown that the discontinuous end configuration is dictated by the nature of the differential equations describing the remodeling process. This process can be considered as a nonlinear dynamical system with many degrees of freedom, which behaves divergent relative to the objective, leading to many possible solutions. The precise solution is dependent on the parameters in the remodeling rule, the load and the initial conditions. The feedback mechanism in the process is self-enhancing, denser bone attracts more strain energy, whereby the bone becomes even more dense. It is suggested that this positive feedback of the attractor state (the strain energy field) creates order in the end configuration. In addition, the process ensures that the discontinuous end configuration is a structure with a relatively low mass, perhaps a minimal-mass structure, although this is no explicit objective in the optimization process. It is hypothesized that trabecular bone is a chaotically ordered structure which can be considered as a fractal with characteristics of optimal mechanical resistance and minimal mass, of which the actual morphology depends on the local (internal) loading characteristics, the sensor-cell density and the degree of mineralization.},
	author = {Weinans, H and Huiskes, R and Grootenboer, H J},
	date-added = {2016-12-22 04:40:28 +0000},
	date-modified = {2016-12-22 04:40:28 +0000},
	journal = {J Biomech},
	journal-full = {Journal of biomechanics},
	mesh = {Bone Density; Bone Remodeling; Bone Resorption; Bone and Bones; Computer Simulation; Elasticity; Femur; Femur Head; Humans; Models, Biological; Periosteum; Stress, Mechanical},
	month = {Dec},
	number = {12},
	pages = {1425-41},
	pmid = {1491020},
	pst = {ppublish},
	title = {The behavior of adaptive bone-remodeling simulation models},
	volume = {25},
	year = {1992}}

@article{Albro09,
	abstract = {This study reports experimental measurements of solute diffusivity and partition coefficient for various solute concentrations and gel porosities, and proposes novel constitutive relations to describe these observed values. The longer-term aim is to explore the theoretical ramifications of accommodating variations in diffusivity and partition coefficient with solute concentration and tissue porosity, and investigate whether they might suggest novel mechanisms not previously recognized in the field of solute transport in deformable porous media. The study implements a model transport system of agarose hydrogels to investigate the effect of solute concentration and hydrogel porosity on the transport of dextran polysaccharides. The proposed phenomenological constitutive relations are shown to provide better fits of experimental results than prior models proposed in the literature based on the microstructure of the gel. While these constitutive models were developed for the transport of dextran in agarose hydrogels, it is expected that they may also be applied to the transport of similar molecular weight solutes in other porous media. This quantification can assist in the application of biophysical models that describe biological transport in deformable tissues, as well as the cell cytoplasm.},
	author = {Albro, Michael B and Rajan, Vikram and Li, Roland and Hung, Clark T and Ateshian, Gerard A},
	date-added = {2016-12-22 04:38:26 +0000},
	date-modified = {2016-12-22 04:38:26 +0000},
	doi = {10.1007/s12195-009-0076-4},
	journal = {Cell Mol Bioeng},
	journal-full = {Cellular and molecular bioengineering},
	month = {Sep},
	number = {3},
	pages = {295-305},
	pmc = {PMC2996616},
	pmid = {21152414},
	pst = {ppublish},
	title = {Characterization of the Concentration-Dependence of Solute Diffusivity and Partitioning in a Model Dextran-Agarose Transport System},
	volume = {2},
	year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s12195-009-0076-4}}

@article{Simo87,
	author = {Simo, JC},
	date-added = {2016-12-22 04:33:15 +0000},
	date-modified = {2016-12-22 04:33:27 +0000},
	journal = {Computer methods in applied mechanics and engineering},
	number = {2},
	pages = {153--173},
	publisher = {Elsevier},
	title = {On a fully three-dimensional finite-strain viscoelastic damage model: formulation and computational aspects},
	volume = {60},
	year = {1987}}

@article{Ateshian15,
	abstract = {This study presents a framework for viscoelasticity where the free energy density depends on the stored energy of intact strong and weak bonds, where weak bonds break and reform in response to loading. The stress is evaluated by differentiating the free energy density with respect to the deformation gradient, similar to the conventional approach for hyperelasticity. The breaking and reformation of weak bonds is treated as a reaction governed by the axiom of mass balance, where the constitutive relation for the mass supply governs the bond kinetics. The evolving mass contents of these weak bonds serve as observable state variables. Weak bonds reform in an energy-free and stress-free state, therefore their reference configuration is given by the current configuration at the time of their reformation. A principal advantage of this formulation is the availability of a strain energy density function that depends only on observable state variables, also allowing for a separation of the contributions of strong and weak bonds. The Clausius-Duhem inequality is satisfied by requiring that the net free energy from all breaking bonds must be decreasing at all times. In the limit of infinitesimal strains, linear stress-strain responses and first-order kinetics for breaking and reforming of weak bonds, the reactive framework reduces exactly to classical linear viscoelasticity. For large strains, the reactive and classical quasilinear viscoelasticity theories produce different equations, though responses to standard loading configurations behave similarly. This formulation complements existing tools for modeling the nonlinear viscoelastic response of biological soft tissues under large deformations.},
	author = {Ateshian, Gerard A},
	date-added = {2016-12-22 04:31:42 +0000},
	date-modified = {2016-12-22 04:31:42 +0000},
	doi = {10.1016/j.jbiomech.2015.02.019},
	journal = {J Biomech},
	journal-full = {Journal of biomechanics},
	keywords = {Mixture theory; Reaction kinetics; Soft tissue mechanics; Viscoelasticity},
	mesh = {Elasticity; Kinetics; Models, Theoretical; Viscosity},
	month = {Apr},
	number = {6},
	pages = {941-7},
	pmc = {PMC4422403},
	pmid = {25757663},
	pst = {ppublish},
	title = {Viscoelasticity using reactive constrained solid mixtures},
	volume = {48},
	year = {2015},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jbiomech.2015.02.019}}

@article{Lai91,
	abstract = {Swelling of articular cartilage depends on its fixed charge density and distribution, the stiffness of its collagen-proteoglycan matrix, and the ion concentrations in the interstitium. A theory for a tertiary mixture has been developed, including the two fluid-solid phases (biphasic), and an ion phase, representing cation and anion of a single salt, to describe the deformation and stress fields for cartilage under chemical and/or mechanical loads. This triphasic theory combines the physico-chemical theory for ionic and polyionic (proteoglycan) solutions with the biphasic theory for cartilage. The present model assumes the fixed charge groups to remain unchanged, and that the counter-ions are the cations of a single-salt of the bathing solution. The momentum equation for the neutral salt and for the intersitial water are expressed in terms of their chemical potentials whose gradients are the driving forces for their movements. These chemical potentials depend on fluid pressure p, salt concentration c, solid matrix dilatation e and fixed charge density cF. For a uni-uni valent salt such as NaCl, they are given by mu i = mu io + (RT/Mi)ln[gamma 2 +/- c(c + cF)] and mu w = mu wo + [p-RT phi (2c + cF) + Bwe]/pwT, where R, T, Mi, gamma +/-, phi, pwT and Bw are universal gas constant, absolute temperature, molecular weight, mean activity coefficient of salt, osmotic coefficient, true density of water, and a coupling material coefficient, respectively. For infinitesimal strains and material isotropy, the stress-strain relationship for the total mixture stress is sigma = - pI-TcI + lambda s(trE)I + 2 musE, where E is the strain tensor and (lambda s, mu s) are the Lam{\'e} constants of the elastic solid matrix. The chemical-expansion stress (-Tc) derives from the charge-to-charge repulsive forces within the solid matrix. This theory can be applied to both equilibrium and non-equilibrium problems. For equilibrium free swelling problems, the theory yields the well known Donnan equilibrium ion distribution and osmotic pressure equations, along with an analytical expression for the "pre-stress" in the solid matrix. For the confined-compression swelling problem, it predicts that the applied compressive stress is shared by three load support mechanisms: 1) the Donnan osmotic pressure; 2) the chemical-expansion stress; and 3) the solid matrix elastic stress. Numerical calculations have been made, based on a set of equilibrium free-swelling and confined-compression data, to assess the relative contribution of each mechanism to load support. Our results show that all three mechanisms are important in determining the overall compressive stiffness of cartilage.},
	author = {Lai, W M and Hou, J S and Mow, V C},
	date-added = {2016-12-22 04:22:59 +0000},
	date-modified = {2016-12-22 04:22:59 +0000},
	journal = {J Biomech Eng},
	journal-full = {Journal of biomechanical engineering},
	mesh = {Biomechanical Phenomena; Cartilage, Articular; Elasticity; Models, Biological; Osmosis; Solutions; Stress, Mechanical},
	month = {Aug},
	number = {3},
	pages = {245-58},
	pmid = {1921350},
	pst = {ppublish},
	title = {A triphasic theory for the swelling and deformation behaviors of articular cartilage},
	volume = {113},
	year = {1991}}

@article{Overbeek56,
	author = {Overbeek, J T},
	date-added = {2016-12-22 04:22:34 +0000},
	date-modified = {2020-08-23 18:44:28 -0400},
	journal = {Prog Biophys Biophys Chem},
	journal-full = {Progress in biophysics and biophysical chemistry},
	keywords = {CHEMISTRY, PHYSICAL},
	mesh = {Chemical Phenomena; Chemistry, Physical; Physical Examination},
	pages = {57-84},
	pmid = {13420188},
	pst = {ppublish},
	title = {The Donnan equilibrium},
	volume = {6},
	year = {1956}}

@article{Carter77,
	abstract = {Compression tests of human and bovine trabecular bone specimens with and without marrow in situ were conducted at strain rates of from 0.001 to 10.0 per second. A porous platen above the specimens allowed the escape of marrow during testing. The presence of marrow increased the strength, modulus, and energy absorption of specimens only at the highest strain rate of 10.0 per second. This enhancement of material properties at the highest strain rate was due primarily to the restricted viscous flow of marrow through the platen rather than the flow through the pores of the trabecular bone. In specimens without marrow, the strength was proportional to the square of the apparent density and the modulus was proportional to the cube of the apparent density. Both strength and modulus were approximately proportional to the strain rate raised to the 0.06 power. These power relationships, which were shown to hold for all bone in the skeleton, allow meaningful predictions of bone tissue strength and stiffness based on in vivo density measurements.},
	author = {Carter, D R and Hayes, W C},
	date-added = {2016-12-22 04:21:10 +0000},
	date-modified = {2016-12-22 04:21:10 +0000},
	journal = {J Bone Joint Surg Am},
	journal-full = {The Journal of bone and joint surgery. American volume},
	mesh = {Animals; Bone and Bones; Cattle; Humans; Stress, Mechanical; Tensile Strength},
	month = {Oct},
	number = {7},
	pages = {954-62},
	pmid = {561786},
	pst = {ppublish},
	title = {The compressive behavior of bone as a two-phase porous structure},
	volume = {59},
	year = {1977}}

@article{Carter76,
	abstract = {The compressive strength of bone is proportional to the square of the apparent density and to the strain rate raised to the 0.06 power. This relationship is applicable to trabecular and compact bone, and provides clinical guidelines for predicting bone strength on the basis of x-ray and densitometric examination.},
	author = {Carter, D R and Hayes, W C},
	date-added = {2016-12-22 04:20:57 +0000},
	date-modified = {2016-12-22 04:20:57 +0000},
	journal = {Science},
	journal-full = {Science (New York, N.Y.)},
	mesh = {Animals; Bone Marrow; Bone and Bones; Cattle; Humans; Stress, Mechanical},
	month = {Dec},
	number = {4270},
	pages = {1174-6},
	pmid = {996549},
	pst = {ppublish},
	title = {Bone compressive strength: the influence of density and strain rate},
	volume = {194},
	year = {1976}}

@article{Ateshian07c,
	abstract = {Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response deltat<Delta(2) / //parallelC(4)//K//, where Delta is a characteristic dimension, C(4) is the elasticity tensor, and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components.},
	author = {Ateshian, Gerard A and Ellis, Benjamin J and Weiss, Jeffrey A},
	date-added = {2016-12-22 04:15:25 +0000},
	date-modified = {2016-12-22 04:16:19 +0000},
	doi = {10.1115/1.2720918},
	journal = {J Biomech Eng},
	journal-full = {Journal of biomechanical engineering},
	mesh = {Animals; Biomechanical Phenomena; Cartilage, Articular; Compressive Strength; Elasticity; Finite Element Analysis; Humans; Mathematics; Models, Biological; Models, Theoretical; Stress, Mechanical; Tensile Strength; Time Factors},
	month = {Jun},
	number = {3},
	pages = {405-12},
	pmc = {PMC3312381},
	pmid = {17536908},
	pst = {ppublish},
	title = {Equivalence between short-time biphasic and incompressible elastic material responses},
	volume = {129},
	year = {2007},
	Bdsk-Url-1 = {http://dx.doi.org/10.1115/1.2720918}}

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